The camera's a good idea - then you've got evidence for a divorce attorney to use.
He's cheating with her, I don't doubt it a bit. Underwear under the bed, the same bed you can smell her perfume in? A "lunch" with phones off? Who does that? Cheating people do.
Breathing heavily when answering the phone, and she's "not there"?
Oh please. If none of that has convinced you, then the camera will.